A new analytical solution of the heat diffusion equation under specific boundary conditions is proposed. The solved problem is the flow of heat in a one-dimensional (1D) solid whose ends are in mediums at prescribed temperatures which follow a sinusoidal law in-phase. Heat is transferred by convection between the ends of the domain and the mediums. The solution is extended to other temperatures of the mediums through the discrete Fourier transformation. Moreover, several heat transfer mechanisms were accounted for by computing an equivalent temperature of the mediums. The performance of the new model was assessed by computing the recorded temperatures at an arch dam case study. Temperatures were computed by: (a) the new 1D analytical model, (b) an improved version of the 10 analytical solution proposed by Stucky and Derron, and (c) a three-dimensional finite element model. The root mean squared error of computed temperatures was 1.23 K for model (a), 3.92 K for (b), and 0.83 K for (c). The new model provided a much better performance than (b) and similar but poorer than (c). (C) 2015 Elsevier Ltd. All rights reserved.
A new analytical solution of the heat diffusion equation under specific boundary conditions is proposed. The solved problem is the flow of heat in a one-dimensional (1D) solid whose ends are in mediums at prescribed temperatures which follow a sinusoidal law in-phase. Heat is transferred by convection between the ends of the domain and the mediums. The solution is extended to other temperatures of the mediums through the discrete Fourier transformation. Moreover, several heat transfer mechanisms were accounted for by computing an equivalent temperature of the mediums. The performance of the new model was assessed by computing the recorded temperatures at an arch dam case study. Temperatures were computed by: (a) the new 1D analytical model, (b) an improved version of the 10 analytical solution proposed by Stucky and Derron, and (c) a three-dimensional finite element model. The root mean squared error of computed temperatures was 1.23 K for model (a), 3.92 K for (b), and 0.83 K for (c). The new model provided a much better performance than (b) and similar but poorer than (c). (C) 2015 Elsevier Ltd. All rights reserved. Read More
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